A curve between two points along which a body can move under gravity in a shorter time than for any other curve.
- ‘An inverted cycloid is the brachistochrone, that is the curve between two points in a vertical plane, along which a bead needs the shortest time to travel.’
- ‘The brachistochrone is a cycloid, but that cycloid is not the only curve satisfying the equation.’
- ‘The brachistochrone problem was one of the earliest problems posed in the calculus of variations.’
- ‘Further enhancements will guide the user through the development of brachistochrones for force fields which differ from gravitational force fields.’
- ‘Here one can see a graph of the brachistochrone for the given endpoint.’
Late 18th century: from Greek brakhistos shortest + khronos time.